Papers

The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers. We measure the singular-value spectra of all four mode unfoldings on Mistral-7B-v0.3 and LLaMA-2-13B and compare four standard tensor decompositions: Tucker, CP, tensor train, and t-SVD, at matched storage. The spectra partition the four axes into two classes. The token and feature modes carry low-rank structure, particularly for keys. The head and layer modes are nearly full-rank and resist compression at any practical error level. Among the four decompositions, Tucker achieves the lowest reconstruction error at every compression ratio from $2\times$ to $5\times$, because it can leave the full-rank modes untouched. Comparisons with two-dimensional unfolding baselines show that the preferred representation differs between keys and values: 2D methods achieve lower key error, while four-way Tucker achieves lower value error at matched storage. A mode-pinning theorem certifies the full-rank preservation from the measured spectra alone. Two further spectral properties affect the compressible modes without touching the full-rank ones: values reach a higher error floor than keys at every ratio, and post-RoPE keys lose $41\%$ - $64\%$ of their pre-RoPE compressibility on both models.

For every fixed integers $r \ge 4$ and $2 \le k \le r-2$, we construct $r$-dimensional cubical sheaf complexes whose degree-$k$ CSS codes have positive constant rate, linear distance, and constant soundness, with bounded row and column weights. Taking $r=4$ and $k=2$ gives a family of asymptotically good binary qLTCs. At the core of our construction is a uniform product-expansion theorem for explicit Reed-Solomon codes on norm-one evaluation sets. The key point is that the expansion constant stays bounded away from zero as the local code lengths grow. We place these codes on arithmetic cubical complexes, obtaining constant local expansion for both the resulting sheaf and its dual. Together with the local-to-global framework of Dinur, Lin, and Vidick (FOCS 2024) and sheaf duality, this gives linear distance and constant soundness, while an asymmetric choice of local code dimensions gives positive rate. The resulting codes are explicit and polynomial-time computable.

Providing personalized exoskeleton assistance across varying walking speeds remains challenging. Existing online optimization methods are sample-inefficient, requiring extensive human-in-the-loop (HIL) evaluations to optimize the entire assistive torque profile. Sim-to-real reinforcement learning (RL) offers a promising alternative but cannot directly account for individual user preferences. We propose a framework integrating sim-to-real RL with online preference learning for personalized exoskeleton assistance. Specifically, assistance timing is learned in simulation by training RL policies with human musculoskeletal models across varying walking speeds. The learned policies are then distilled and deployed on a physical hip exoskeleton using onboard sensory observations. Gaussian-process-based preference learning further personalizes the assistance magnitude through pairwise user comparisons. By decoupling assistance timing learning in simulation from magnitude optimization in real-world experiments, our framework substantially reduces the online optimization space. Human-subject experiments demonstrate efficient identification of personalized assistive torque profiles across varying walking speeds with fewer real-world evaluations.

We investigate whether state-of-the-art large language models (LLMs) generate feedback that reflects the pedagogical practices of expert teachers in terms of feedback focus and adaptivity. Previous evaluation efforts have examined feedback characteristics, its impact on learning, and its target, yet the focus of feedback and its adaptivity remains largely overlooked. To bridge this gap, we adopt and refine Narciss's taxonomy into seven feedback focus types to annotate teacher and LLM-generated feedback across three university writing courses. We release FeedType, a benchmark containing annotated teacher and LLM feedback from six LLMs under three prompting strategies. We assess the coverage and distribution of feedback focus types, and examine whether LLMs adapt their feedback across draft stages and student performance levels as an expert instructor does. Our findings show that while most LLMs cover most feedback focus types, they fail to reflect teacher feedback distributions and show varying levels of adaptivity, with none matching the teachers' adaptive behavior. We believe FeedType will support future research on pedagogical alignment in LLM feedback generation.

We investigate the topological classification and properties of nonabelian vortices that arise in a 2-dimensional film of a two-component condensate. For a repulsive interaction between the condensates, we realize an order parameter in the ordered configuration space of three complex numbers $\mathcal C_3(\mathbb C)$. Analyzing the homotopic properties, we find the emergence of elementary nonabelian vortex-antivortex pairs connected by energetic strings that are rooted in the repulsive interaction and carry the nonabelian information. Moreover, we predict the existence of Brunnian vortices, which are textures exhibiting zero net winding of the condensate phases and can only be detected by a higher-order winding number. Finally, to motivate technological applications rooted in nonabelian vortex transport, we devise a nonvolatile memory storage device that encodes topologically robust information.

We study two-dimensional steady gravity water waves with general vorticity in a homogeneous, inviscid fluid of finite depth, subject to a surface pressure that tends to distinct constants upstream and downstream. Starting from a fixed supercritical shear flow, we construct two global branches of monotone fronts connecting distinct laminar states, with increasing and decreasing profiles corresponding to the two signs of the pressure transition. Small-amplitude fronts are first obtained via the implicit function theorem and then extended by analytic global continuation.

The lettericity of a graph $G$ is the smallest size of a set $\Sigma$ such that there exist $w_1, \ldots, w_{|V(G)|} \in \Sigma$ and a so-called decoder $D \subseteq \Sigma^2$ for which $G$ is isomorphic to the letter graph $(\{1, \ldots, |V(G)|\}, \{ij : 1 \le i < j \le |V(G)|, w_iw_j \in D\})$. It took around two decades of the study of lettericity for, in the simpler case of paths, a closed-form expression for its lettericity to be derived; this suggests that the question of whether the lettericity of an arbitrary graph can be computed in polynomial time is nontrivial. Indeed, this question has been raised repeatedly as an open problem in recent literature. We solve this problem by showing that the lettericity problem on arbitrary graphs is NP-complete. We also show that each of the natural ways in which a single part of a structure $(\Sigma, w_1, \ldots, w_{|V(G)|}, D)$ witnessing the lettericity could be constrained corresponds to an NP-complete problem, which resolves an additional three open problems from the literature; in particular, we show that the coloring extension, word extension, and decoder extension problems are NP-complete. Additionally, we use the reduction in the NP-completeness proof to give a lower bound on algorithms for lettericity under the Exponential Time Hypothesis (ETH): unless the ETH is false, there cannot exist a deterministic algorithm to decide whether the lettericity of an $n$-vertex graph is at most $k$ in time $2^{o(n)}$, even when $n = 6k$. Finally, we complement the known result that Lettericity is fixed-parameter tractable when parameterized by the standard parameter $k$ by providing a fixed-parameter algorithm with respect to the dual parameterization by $n-k$ running in $2^{\mathcal{O}((n-k)^2)} + \mathcal{O}(n)$ time.

Space weather early warning depends on detecting solar wind transients in in-situ measurements at the first Sun-Earth Lagrange point (L1), before they reach Earth. Fixed thresholds can miss combined magnetic and plasma structure, and many learning methods provide a single anomaly score. We present the Physics-Informed Solar-wind Convolutional autoEncoder for Space-weather (PISCES), a convolutional autoencoder trained without catalog labels on OMNI solar wind measurements under physics constraints. Its loss includes magnetic field consistency, an empirical relation between temperature and velocity, the Parker spiral angle, and penalties on changes between consecutive one-minute samples in derived quantities calculated from the reconstruction. At inference, PISCES separates the anomaly score into magnetic and plasma reconstruction errors, physics relations, and residual corrections, and reports the magnitude of each contribution. Attenuation of the skip connections, selected on validation data, improves average precision for the trained models, while the untrained scores remain nearly the same. The trained models also give a more consistent ordering of these physical contributions. After smoothing with a trailing median, the alarms can precede independently observed sudden commencements, including positive sudden impulses.

We investigate a route to enhanced thermoelectric energy conversion in nanoscale systems by exploiting a correlated quasiperiodic energy landscape in a one-dimensional chain coupled to source and drain reservoirs. The considered modulation generates a highly non-uniform electronic transmission spectrum, providing favorable conditions for achieving a large thermoelectric figure of merit. By systematically tuning the incommensurability parameter, a variety of quasiperiodic configurations are explored, several of which yield high values of the figure of merit exceeding $2$. Electronic transport properties are evaluated within a tight-binding framework using the non-equilibrium Green's function formalism, while the thermoelectric coefficients, including electrical conductance, Seebeck coefficient, and electronic thermal conductance, are determined through the Landauer approach. The underlying quasiperiodic potential belongs to the Aubry-André-Harper (AAH) family and exhibits a weakly varying spatial profile, leading to transmission characteristics that are favorable for thermoelectric optimization. The influence of phonon thermal conductance on the overall energy-conversion efficiency is also analyzed in detail. For the sake of completeness, we also critically inspect the effect of conductor to electrode coupling and the coupling asymmetry on $ZT$. We also check the thermoelectric response of conventional AAH system and an elaborate comparison is made with our chosen quantum system. Our findings highlight the potential of correlated quasiperiodic nanostructures as promising candidates for efficient thermoelectric applications.

We study pairs consisting of a rational isosceles triangle and a rational triangle having a prescribed angle $\theta$, with equal perimeter and equal area. Writing $\rho=\cos(\theta)\in\mathbb{Q}$, we obtain a two-parameter description of the solutions and, for fixed $\rho$, a family of curves $C_\rho$ which are generically of genus $2$. We determine the two singular specializations: there is no genuine pair for $\rho=\frac{1}{2}$, while $\rho=\frac{47}{49}$ admits infinitely many genuine pairs. We completely parametrize two natural one-parameter families in which the $\theta$-triangle is isosceles, and prove several density results for values of $\rho$ admitting one or more genuine pairs. For thirty-five explicit values of $\rho$, Chabauty–Coleman computations determine $C_\rho(\mathbb{Q})$ completely and show that the corresponding pair is unique up to homothety. We also study multiplicity when one triangle is fixed; the condition for a scalene $\theta$-triangle to have two isosceles partners leads to an elliptic $K3$ surface and yields a dense set of such values of $\rho$. Finally, we construct infinite families with at least four genuine pairs and exhibit examples carrying at least five, and in two cases at least six, genuine pairs.

Nature, at the shortest distances accessible to contemporary colliders, is described by the Standard Model of particle physics with remarkable precision. Since the discovery of the Higgs boson in 2012, progress has shifted from finding new resonances to precision studies of established theory. Here, quantum chromodynamics (QCD), describing the interactions of quarks and gluons, plays a central role. Collider observables involving hadrons are made theoretically accessible by factorization, which separates universal long-distance hadron dynamics encoded in parton distributions from process-specific short-distance coefficients calculable in perturbation theory. This thesis develops analytic methods for perturbative QCD with applications to collider phenomenology and proton structure. A major part is devoted to angular integrals, key building blocks of phase-space integrals. Methods originally developed for Feynman integrals, including integration-by-parts identities, expansion by regions, differential equations, and dimensional shifts, are adapted to angular integrals and yield several new results. The analytic structure of one-loop integrals is also studied, with spurious branch cuts removed using single-valued polylogarithms, leading to a compact representation of coefficient functions for semi-inclusive deep-inelastic scattering. A systematic expansion in higher powers of transverse momentum is developed and applied to the Drell-Yan process, refining the understanding of its factorization structure. Finally, a new semi-analytical ansatz for the evolution of parton distributions is explored. Together, these methods improve analytic control over radiative corrections, kinematic dependence, and scale evolution in processes relevant to the Electron-Ion Collider and other collider experiments.

We classify all $D(u^2)$-triples of triangular numbers whose smallest element is $T_{4u-1}$ or $T_{4u}$. We study the regularity of $D(N)$-triples of triangular numbers. We also show that infinitely many positive integers $u$ admit an all-triangular $D(u^2)$-quadruple. For every positive integer $k$, triangular number $T_{16k^2-1}$ belongs to infinitely many $D(u^2)$-quadruples of triangular numbers with distinct positive integer parameters $u$.

The discovery of billion solar mass black holes at high redshift challenges any standard Eddington-limited growth model. Previous work has shown that an advective accretion disk can account for these early black holes with episodic accretion. It has also been shown that if the accretion disk of a black hole is misaligned from the spin axis of the black hole, the disk can become advective within a certain radius. While warped and misaligned accretion disks have been explored in numerical simulations, there is no fully or semi-analytic framework that self-consistently connects disk warp, mass inflow, winds, and energy transport in the super-Eddington regime. In this work, we develop a first-principles semi-analytic model of a radiation-pressure-dominated, warped accretion disk, starting from the coupled conservation equations for mass, energy, and angular momentum. We find profiles for the radial velocity and surface density that explicitly account for disk warping and mass loss and determine the radius at which the disk becomes advective. We explore changes with black hole spin, misalignment angle and viscosity, reproducing relevant results from numerical studies.

This paper has two aims. First, we study nowhere-zero flows in countably infinite graphs, observing the different roles played by two types of bridge. Second, we ask how typical graphs with such bridges are. Since there is no canonical probability measure on countable graphs, we explore an analytic approach and study which graph classes are nowhere dense and which are meager for two different definitions of a distance. We characterize in this sense graphs with a bridge (separating a finite component, or two infinite ones), $D$-edge-colorable graphs, etc.

Data assimilation estimates a dynamical state from partial and noisy observations. Classical ensemble filters are efficient but restrict analysis updates through finite sample covariance and affine Gaussian distribution. We introduce the Flow Ensemble Filter (FlowEF), which uses conditional flow matching to transport the forecast ensemble from a classical baseline filter to an analysis ensemble. FlowEF uses a localized Gaussian source during training, transports forecast ensemble members from a baseline filter at deployment, and conditions its velocity field on ensembles from that baseline filter and the observation. The proposed model therefore learns a nonlinear update while mapping each baseline ensemble independently. For sparsely observed dynamical systems, FlowEF improves both deterministic and probabilistic metrics over all four classical ensemble filters. It also achieves the best performance among the state-of-the-art generative data assimilation models.

We define a Bergman barycentric extension of boundary homeomorphisms of the complex unit ball by \[ E_B(f)(z)=\barB(f_*\sigma_z), \] where \(\barB\) is the Busemann barycenter for the Bergman metric and \(\sigma_z\) is the visual, equivalently Poisson–Szegő, measure based at \(z\). We prove well-definedness, prescribed boundary values, full \(\Aut(\B^n)\)-naturality, and interior real-analyticity. For every CR-quasisymmetric boundary homeomorphism, the Bergman barycentric extension is a quasi-isometry of complex hyperbolic space; moreover \(E_B(f^{-1})\) is a coarse inverse of \(E_B(f)\). Under sufficiently small positive CR cross-ratio distortion we obtain a sharper Tukia-type theorem: for every \(M>1\), the extension is a real-analytic diffeomorphism satisfying \[ M^{-1}d_B(x,y)\le d_B(E_B(f)(x),E_B(f)(y))\le M d_B(x,y). \] In contrast, for \(n\ge2\) there are smooth CR-orientation-preserving CR-quasisymmetric boundary diffeomorphisms whose barycentric extensions are non-injective and, after normalization, have singular differential. Thus large-scale quasi-isometric control persists on the full CR-quasisymmetric class, whereas local non-degeneracy requires stronger boundary control.

Machine-learned interatomic potentials (MLIPs) enable simulations of larger atomistic systems over longer timescales than traditional ab initio methods but require large, diverse training data. Existing datasets lack comprehensive sampling of solid-liquid interfaces, which exhibit complex phenomena such as solvent layering and surface reconstruction critical for energy and catalytic materials. Here, we present SoLiD26, a curated solid-liquid interface dataset of 15.4 million first-principles structures with up to 576 atoms and 15 chemical elements for training and evaluating MLIPs. The structures were compiled from density functional theory (DFT) calculations, with most configurations originating from ab initio molecular dynamics (AIMD) simulations. SoLiD26 includes aqueous coinage metal interfaces, electrode-electrolyte systems, and selected bulk reference structures, calculated with VASP using the PBE functional and D3 dispersion corrections. The application of SoLiD26 for training and evaluating MLIPs is demonstrated with a suite of MACE models on a simple training, validation and test split. This dataset provides a valuable resource for advancing MLIP development targeted at modelling solid-liquid interfaces in electrochemical and catalytic systems.

Twist-bend nematics formed by achiral particles support heliconical domains of opposite handedness. Using Monte Carlo and molecular dynamics simulations of repulsive bent particles, we study the interface between two such domains. Rather than a gradually untwisting texture, we find a density-modulated splay-bend-twist structure. The density modulation is along the helix axis with a period of approximately half the bulk pitch, while the twist is locally enhanced in magnitude, alternates in sign, and vanishes only on an undulating surface. An explicit director interpolation shows how gradients along the helix axis and across the interface combine to produce an undulating zero-twist surface.

We introduce the notion of factorizable Lie conformal bialgebras and establish their correspondence with quadratic Rota-Baxter Lie conformal algebras of nonzero weight. Consequently, on the one hand, a Lie conformal bialgebra with a Rota-Baxter operator of nonzero weight gives a factorizable Lie conformal bialgebra. And on the other hand, as the conformal analogue of the fact that a quadratic Rota-Baxter Lie algebra induces a generalized pseudo-Hessian post-Lie algebra and a special partial-pre-post-Lie algebra, a quadratic Rota-Baxter Lie conformal algebra as well as a factorizable Lie conformal bialgebra induces a generalized pseudo-Hessian post-Lie conformal algebra and a special partial-pre-post-Lie conformal algebra. Furthermore, we generalize the correspondence between Gel'fand-Dorfman bialgebras and a class of Lie conformal bialgebras to the factorizable cases. There is not only a correspondence between factorizable Gel'fand-Dorfman bialgebras and a class of factorizable Lie conformal bialgebras, but also a correspondence for their corresponding quadratic Rota-Baxter counterparts as well as some induced structures. In particular, there is a construction of factorizable Lie conformal bialgebras from Gel'fand-Dorfman bialgebras with a Rota-Baxter operator of nonzero weight.

We investigate the computation of optimal bias potentials for accelerating transitions between metastable states and for computation of equilibrium properties in molecular dynamics simulations. We formulate optimal biasing as an ergodic optimal control problem (OCP), which can be recast as a linear eigenvalue problem for the infinitesimal generator of the unbiased dynamics. We demonstrate that data-driven learning methods for the generator enable reliable solution of the OCP, computation of biasing potentials, extraction of equilibrium properties, and acceleration of state transitions. We also explore the relation of the control problem to coarse grained representations and learning of coarse grained dynamics.

We prove local well-posedness for the initial-boundary-value problem for the Korteweg–de Vries equation on the right half-line at the critical regularity $s=-3/4$, with initial and boundary data in $H^{-3/4}(\mathbb R_+)$ and $H^{1/12}(\mathbb R_+)$, respectively. This reaches the endpoint left open in the previous half-line results of Holmer (2006) and Bona, Sun, and Zhang (2006), who established local well-posedness for $s>-3/4$. The proof is based on a contraction argument in the Besov-type Bourgain space introduced by Kishimoto. The main difficulty is to construct a boundary forcing operator compatible with the endpoint $b=1/2$ and the required $\ell^1$-summability in the modulation variable. We construct such an operator using a Laplace-transform representation of the linear half-line problem and a carefully designed extension to $x<0$. The extension combines the required regularity across the boundary with prescribed vanishing spatial moments, yielding favorable low-frequency behavior of the associated kernel. A pointwise kernel estimate then provides the crucial dyadic summability needed for the $X^{-3/4,1/2,1}$ estimate. Together with a time-trace estimate for the Duhamel term at $b=1/2$, this yields the critical local well-posedness result. The ideas used here have prospects to be used in other nonlinear dispersive equations on the half-lines.

Automatic pitch correction (APC) requires distinguishing the unintended intonation errors from expressive pitch variation. Existing systems either lack explicit harmonic modeling, as vocal-only methods do, or do not directly use the note-level polyphonic context. Therefore, we propose MIDIBack, a note-level APC framework that jointly models the vocal and accompaniment events in a shared OctupleMIDI sequence. We evaluate MIDIBack under 6 note corruption regimes, including global outshift, learned note-dependent detuning, uniform perturbations, and their combinations. The resulting model achieves 78.6% overall raw pitch accuracy (RPA), and 81.5% under combined global outshift and learned detuning. Removing the accompaniment conditioning reduces RPA from 81.5% to 35.8% in outshift, showing the effectiveness of accompaniment context. Case studies on accompaniment modulation further illustrate that vocal note predictions

Most Turkish-capable large language models (LLMs) are evaluated using general-purpose benchmarks rather than long, structurally complex domain documents. This paper evaluates five open-weight 7B-8B models for Turkish document question answering under a resource-constrained local deployment setting. The primary benchmark contains 100 systematically validated questions derived from a 109-page industrial R&D report, and the evaluation protocol is replicated using a second 112-page public-sector report and an independently constructed 100-question set. All models are evaluated locally on an NVIDIA RTX 3050 laptop GPU with 6 GB VRAM using controlled prompting, decoding, and 4-bit quantisation. The principal methodological contribution is an evidence-annotated evaluation protocol that separates retrieval failure from downstream model reasoning failure without requiring additional model calls. On the primary benchmark, end-to-end accuracy ranges from 49% to 75%. Seven lexical, dense, and hybrid retrieval configurations are additionally compared using 95% Wilson intervals and exact paired McNemar tests; none significantly outperforms the character TF-IDF baseline on either document. Evidence recall saturates differently across the two reports, showing that retrieval and effective context capacity can be binding constraints for some documents but not others. These results demonstrate that model selection, retrieval behaviour, and hardware limits must be evaluated separately when deploying open-weight LLMs for Turkish domain documents.

Decoder-only Transformer language models cache keys and values (KV) to reuse past computation during generation. Sharing KV across layers saves storage but reduces the diversity of representations available across depth. We study what local memory should retain alongside shared global KV, separating historical content from the input source used to form it. At 126M parameters and 2K context, an eight-seed study finds about 1.4% lower held-out test perplexity with local history than with a current-token local branch. Capacity, entry-count and training-compute controls support the value of historical content. In a two-seed comparison, this value persists when adjacent layers share local inputs while retaining independent projections; source sharing also shortens exact cache-construction dependencies. Against GQA and adjacent-layer KV sharing, equal bounded learning-rate searches and new-seed confirmation yield better same-source likelihood with larger caches and higher long-request latency. The ordering against adjacent-layer sharing persists after equal-token adaptation to 8K, with a short-context cost. The eight-seed external-book history effect remains uncertain, and downstream outcomes vary by task. We derive a sufficient suffix schedule that reduces upper-layer construction work while preserving the complete cache in exact arithmetic.

Givental-Kim and Ciocan-Fontanine gave an explicit presentation of the quantum cohomology ring of the flag variety. The author and Shirato introduced an algebraic generalization of their presentation in the context of the coordinate rings of regular nilpotent Hessenberg varieties. In particular, they connect the coordinate ring of the lower unipotent group in a general linear group and the polynomial ring with quantum parameters. In this paper we consider the dual of the connection and we see that the Plücker coordinates correspond to the quantizations of Schur polynomials. As an application of the connection, we construct an action of the symmetric group on the polynomial ring with quantum parameters. Using the symmetric group action, one can define the divided difference operators on the polynomial ring with quantum parameters. We study the quantizations of Schubert polynomials in relation to the divided difference operators.

Effective summarization of interrogative dialogues is a critical task in forensic and investigative settings, requiring high factual accuracy, coherence, and attribute-specific relevance. In this work, we introduce CASPER, a novel Chain-of-Thought Attribute-Specific Prompting for Evaluative Summarization framework that leverages structured prompting and iterative refinement to generate high-quality summaries of interrogator-witness interactions. We construct MINDSum, a dataset extending the MIND corpus, comprising 6,000 utterance pairs annotated with event details, factual statements, character descriptions, and fillers. CASPER employs RoleEval, a hierarchical evaluation mechanism where multiple roles (officer, inspector, senior inspector) iteratively assess summaries based on predefined criteria. By integrating entity extraction and structured feedback loops, CASPER significantly improves factual consistency and contextual completeness compared to existing baselines. Experimental results demonstrate that our framework outperforms standard summarization models on both lexical (ROUGE) and semantic (BERTScore) metrics, while human evaluation confirms its alignment with expert reasoning. Our findings underscore the potential of controlled summarization in high-stakes domains, paving the way for AI-driven forensic intelligence.

Small and medium-sized language models offer cost-effective executors for tool-using agents, making them attractive for local and large-scale deployment. However, in long-horizon and stateful environments, they often make structural errors such as missing required observations, performing premature writes, repeating failed calls, and violating action preconditions. These errors can lead to incorrect state updates, policy violations, and costly or irreversible consequences, making reliable tool execution a critical deployment challenge. Existing fine-tuning approaches require substantial data and computation, while flat memory may retrieve failed actions without preserving their causal context or safety conditions. In this paper, we propose FRESH, a Failure-aware Retrieval framework over Experience-Structured Heterogeneous graphs, which transforms historical successes and failures into structured external experience for tool-using agents. By explicitly modeling the dependencies among tasks, actions, errors, repairs, and execution conditions, FRESH helps frozen language models reuse reliable strategies, avoid recurring failures, and make safer decisions in stateful tool interactions. Experiments on $\tau$-Bench and AppWorld with multiple open-source models show that FRESH consistently improves task success and tool-use reliability over no-memory agents and representative memory-based baselines.

This paper presents an LLM-assisted workflow for visualizing structural differences in evolving software require- ments. Implemented in the OntologyWeb environment, the work- flow represents baseline and current requirements as triple-based semantic graphs and supports side-by-side comparison of curated graph snapshots. The comparison view aligns matched entities and uses visual encoding to highlight structural changes.

Stellar flares are important tracers of magnetic activity and can significantly influence the characterization of exoplanet host stars by introducing time-dependent astrophysical variability. ESA's Ariel mission, designed for atmospheric characterization of exoplanets, will include the VISPhot instrument, providing high-cadence optical photometry offering an opportunity to study stellar flares while identifying and mitigating their impact on transit spectroscopy. We discuss Ariel's potential for flare studies, emphasizing the importance of short-cadence observations for resolving flare morphology and estimating flare energies. We identify potential flaring targets within the Ariel Mission Candidate Sample by cross-matching it with a TESS-based flare catalog, identifying 44 stars in the sample of 3321 host stars with flare rates spanning 0.0012-1.05 flares per day yielding a lower limit. The majority of these active stars are expected to flare infrequently during typical Ariel observations, but for a few of the most active targets there is a significant chance of flaring during a typical Ariel observing window. We further investigate the detectability of stellar flares in Ariel's wavelength range using synthetic spectra based on time-dependent RADYN flare models propagated through the Ariel radiometric simulator. Our simulations indicate that strong flares on cool dwarfs can produce measurable infrared signatures, with flux variations reaching several percent, substantially exceeding the amplitudes of typical exoplanet atmospheric features. These results demonstrate stellar flares represent both a valuable ancillary science case and a potential source of contamination for Ariel observations, highlighting the need for improved flare models and mitigation strategies to maximize the mission's scientific return.

Helical dichroism (HD), arising from the interaction between structured light carrying orbital angular momentum (OAM) and chiral matter, offers opportunities for enhanced chiroptical characterization at the subwavelength scale. Here, we employ inverse design to develop chiral metasurfaces tailored for enhanced HD under Laguerre-Gaussian (LG) beam illumination. The optimized planar structure exhibits a simulated HD around 115% at 800 nm for opposite OAM states, revealing the strong chiroptical response enabled by the inverse-designed geometry. The optimized metasurfaces were fabricated from Si$_3$N$_4$ and experimentally characterized using a custom-built optical system with controlled OAM excitation. A single chiral metasurface exhibited a maximum experimental HD up to 62% near 800 nm, demonstrating a strong OAM-dependent helical dichroic response from a single 6-micron-large chiral structure. Although the measured HD value is lower than the optimized simulation value, the experimental result validates the feasibility of inverse-designed chiral metasurfaces for structured-light chiroptics. These findings establish inverse design as an effective approach for engineering compact chiral nanophotonic structures with enhanced interactions with structured light, offering potential for miniaturized chiroptical sensing and OAM-resolved imaging.